The value of a car decreases by 20% per year Mr. Singh for purchase is a $22,000 automobile what is the value of the car the end of the second year

Answers

Answer 1

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &22000\\ r=rate\to 20\%\to \frac{20}{100}\to &0.20\\ t=\textit{elapsed time}\to &2\\ \end{cases} \\\\\\ A=22000(1-0.2)^2[/tex]

Answer 2

Answer: the answer is $26,400

Step-by-step explanation:

Related Questions

How long will it take a $800 investment to be worth $900 if it is continuously compounded at 11% per year?

Answers

Final answer:

It takes approximately 1.083 years, or around 1 year and 1 month for an $800 investment to grow to $900 when continuously compounded with an 11% yearly interest rate.

Explanation:

To calculate how long it will take for an $800 investment to grow to $900 with continuous compounding at an 11% yearly interest rate, we use the formula for continuously compounded interest, P = Pert, where P is the final amount, Pe is the original principal, r is the interest rate, and t is time in years.

Rearranging the equation to find t, we have, t = ln(P/Pe) / r.

Substitute P as $900, Pe as $800, and r as 0.11 into the formula.

Therefore, t = ln(900/800) / 0.11 = approximately 1.083 years or around 1 year and 1 month.

Learn more about Continuous Compound Interest here:

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A parallelogram is cut out of a 12-inch by 8-inch sheet of paper. There are four right triangle remnants. Two have the dimensions 2 inches by 9 inches, and the other two have the dimensions 3 inches by 6 inches. The resulting parallelogram has a base of approximately 9.22 inches. Complete the following steps to calculate the altitude of the parallelogram using area methods. The area of the sheet of paper is square inches. The combined area of the triangle cutouts is square inches. The area of the parallelogram is square inches. The altitude of the parallelogram rounded to two decimals is square inches.

Answers

Answer:

6.51

Step-by-step explanation:

The area of a shape is the amount of space it occupies.

The area of the paper is 96 square inchesThe combined area of the triangle cutouts is 36 square inchesThe area of the parallelogram is 60 square inchesThe altitude of the parallelogram is 6.51 inches

The dimension of the paper is given as: 12-inch by 8-inch

So, its area is:

[tex]\mathbf{A_1 =12 \times 8}[/tex]

[tex]\mathbf{A_1 =96}[/tex]

The dimensions of the 4 right triangles are: Two 2 inches by 9 inches, and two 3 inches by 6 inches

So, the combined area is:

[tex]\mathbf{A_2 = 2 \times \frac 12 \times 2 \times 9 + 2 \times \frac 12 \times 3 \times 6}[/tex]

[tex]\mathbf{A_2 = 36}[/tex]

The area of the parallelogram is the difference between the areas of the paper and the four right triangles.

So, we have:

[tex]\mathbf{A_3 = A_1 - A_2}[/tex]

[tex]\mathbf{A_3 = 96 - 36}[/tex]

[tex]\mathbf{A_3 = 60}[/tex]

The area of a parallelogram is:

[tex]\mathbf{Area = Base \times Altitude}[/tex]

The base is given as 9.22

So, we have:

[tex]\mathbf{60 = 9.22\times Altitude}[/tex]

Divide both sides by 9.22

[tex]\mathbf{6.51 = Altitude}[/tex]

Rewrite as:

[tex]\mathbf{Altitude = 6.51}[/tex]

Hence, the altitude of the parallelogram is 6.51 inches

Answers

First, transform the height to SI unit (meter):
1 feet = 0.3048 m
12 feet = 12 x 0.3048 = 3.6576 m

For a vertical jump:
velocity = sqrt(2gh) = sqrt(2 x 9.8 x 3.6576) = 8.4669 meter/second

Therefore, at an angle of 45 degrees:
velocity = vertical velocity / sin(45)
= 8.4669 / sin(45)
= 11.974 meter/second

Jessica and Franklin are volunteering to paint one of their community member’s fences for service hours. If Jessica could complete the job in 6 hours and Franklin could complete the job in 4.5 hours, how long would it take them to complete the job together, to the nearest minute?

Answers

2.57 hours approximately

[tex] \frac{1}{t} = \frac{1}{6} + \frac{1}{4.5} = \frac{3+4}{18} = \frac{7}{18} [/tex]
t=18/7=2.57 hour =154 min

what is 8m-3-7m???????

Answers

If Your Simplifying The Answer Is m = 6
8m + -3 = 3 + 7m Hope I helped

Answer:

i personally think it's 4

Step-by-step explanation:

even tho this was 4 years ago ehhhhhhh

find the poin on the graph 0f f(x)=1-x^2 that are closest to0(0,0)

Answers

Represent any point on the curve by (x, 1-x^2). The distance between (0, 0) and (x, 1-x^2) is

[tex] \sqrt{(x-0)^2+(1-x^2-0)^2}=\sqrt{x^2+(1-x^2)^2}=\sqrt{x^2+1-2x^2+x^4} [/tex]

To make this easier, let's minimize the SQUARE of this quantity because when the square root is minimal, its square will be minimal.

So minimize [tex]L=x^4-x^2+1[/tex]

Find the derivative of L and set it equal to zero.

[tex]\frac{d}{dx}(L)=4x^3-2x \\ 4x^3-2x=0 \\ 2x(2x^2-1)=0[/tex]

This gives you [tex]x=0[/tex] or [tex]x^2=\frac{1}{2} \\ x=\pm\sqrt{2}/2[/tex]

You can use the Second Derivative Test to figure out which value(s) produce the MINIMUM distance.

[tex]\frac{d^2}{dx}=12x^2-2[/tex]

When x = 0, the second derivative is negative, indicating a relative maximum. When [tex]x=\pm\frac{\sqrt{2}}{2}[/tex], the second derivative is positive, indicating a relative MINIMUM.

The two points on the curve closest to the origin are [tex]\left( \pm\frac{\sqrt{2}}{2},\frac{1}{2} \right)[/tex]

How many numbers are between 0 and 1/10

Answers

Infinitely in theory.

If a cow has a mass of 9×1029×102 kilograms, and a blue whale has a mass of 1.8×1051.8×105 kilograms, which of these statements is true?

A.) The blue whale has about 200200 times more mass.
B.)The blue whale has about 500500 times more mass.
C.)The cow has about 200200 times more mass.
D.)There is no way to compare the masses.

Answers

cow : 9 x 10^2 = 9 * 100 = 900
whale : 1.8 x 10^5 = 1.8 * 100,000 = 180,000

180,000/900 = 200

The blue whale has about 200 times more mass <==

Answer:

The blue whale has about 200 times more mass.

identity the two rational numbers

Answers

B and D are both rational.

A rational number is a number that can be represented as a ratio fo two integers.

-7/3 is rational because both -7 and 3 are integers. 2.777... equals 25/9. 25 and 9 are both rational numbers.

One 16-ounce bottle of an energy drink has an average of 500 mg of caffeine with a standard deviation of 25 mg. In a carton containing 30 bottles, what is the standard deviation of the average amount of caffeine?

Answers

Final answer:

The standard deviation of the average amount of caffeine in a carton containing 30 bottles of an energy drink is approximately 4.564 mg.

Explanation:

To calculate the standard deviation of the average amount of caffeine in a carton containing 30 bottles of an energy drink, we can use the concept of the sampling distribution of the sample mean.

When independent random samples of a fixed size are taken from a population, the standard deviation of the sample means (σx-bar) is equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is also known as the standard error of the mean.

The formula to find the standard deviation of the sample means is:

σx-bar = σ / √n

In this case, the population standard deviation is given as 25 mg of caffeine, and the sample size is 30 bottles.

So, we calculate the standard deviation of the average amount of caffeine as follows:

σx-bar = 25 mg / √30

σx-bar ≈ 25 mg / 5.477

σx-bar ≈ 4.564 mg (rounded to three decimal places)

Thus, the standard deviation of the average amount of caffeine in a carton containing 30 bottles is approximately 4.564 mg.

Allen's monthly take-home pay is $3000, and his monthly rent is $750. If both his monthly take-home pay and his rent increase by $200, what percentage of Allen's take-home pay will be used to pay rent?

Answers

well, if they both increase by 200 each, that means his take-home pay is 3200 and his rent is 950

ok... if we take 3200 as the 100%, what is 950 in percentage of it?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 3200&100\\ 950&x \end{array}\implies \cfrac{3200}{950}=\cfrac{100}{x}[/tex]

solve for "x".

Answer:

29.68%

Step-by-step explanation:

Allen's monthly take-home pay is $3000

His monthly rent is $750

Now both his monthly take-home pay and his rent increase by $200

So, After increase Allen's monthly take-home pay =$3000+$200= $3200

After increase His monthly rent = $750+200=$950

Now we are supposed to find what percentage of Allen's take-home pay will be used to pay rent

So, percentage = [tex]\frac{\text{Rent after increase}}{\text {Take- home pay after increase}} \times 100[/tex]

= [tex]\frac{950}{3200}\times 100[/tex]

= [tex]\frac{950}{32}[/tex]

= [tex]29.68\%[/tex]

Hence 29.68% of Allen's take-home pay will be used to pay rent.

the directions for mixing water and powdered milk say that one should use 3 cups of water for each cup of powdered milk. how many cups of powdered milk are needed if 5 cups of water are used

Answers

Set up conversion problems so that you can cancel out units that you don't want and introduce units that you do want for your final solution.

5w(m/3w)=15m

So you will need 15 cups of milk if 5 cups of water are used.

Trapezoid ABCD is similar to rectangle EFGH. Side CD is proportional to side ___.

Answers

Side CD is proportional to side GH

We deal from a well-shuffled 52-card deck. calculate the probability that the 13th card is the first king to be dealt.

Answers

Final answer:

The probability that the 13th card is the first king to be dealt is 1/52.

Explanation:

To calculate the probability that the 13th card is the first king to be dealt from a well-shuffled 52-card deck, we need to consider the number of favorable outcomes and the total number of possible outcomes. There are 4 kings in the deck, so the probability of the first king being the 13th card is 1/52.

Final answer:

The probability that the 13th card is the first king to be dealt in a shuffled 52-card deck is 1/13.

Explanation:

In a well-shuffled 52-card deck, the probability that the 13th card is the first king to be dealt can be calculated as follows:

First, let's determine the number of favorable outcomes. Since there are 4 kings in the deck, there are 4 possible kings that can be the first king dealt.

Next, let's determine the number of possible outcomes. Since there are 52 cards in the deck, there are 52 possible cards to be the 13th card dealt.

Therefore, the probability is calculated as:

Probability = Number of favorable outcomes / Number of possible outcomes

Probability = 4 / 52

Probability = 1 / 13

So, the probability that the 13th card is the first king to be dealt is 1/13.

what is the value of -2 x^2 +4y if x = -2 and y =3

Answers

Substitute the values
-2(-2)^2+4(3)
First evaluate the exponent.
-2(4)+4(3)
Then evaluate multiplication.
-8+4(3)
-8+12
Then add.
Final answer:4

You buy a pair of jeans at a department store. Jeans 39.99 Discount -10.00 Subtotal 29.99 Sales tax 1.95 Total 31.94 a. What is the percent of discount to the nearest percent? The percent of discount is ___%. b. What is the percent of sales tax to the nearest tenth of a percent? The percent of sales tax is ___% c. The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent? The percent of markup is ___%

Answers

The discount offered on the jeans is 25 percent. The sales tax charged on the jeans is 6.5 percent. Markup on the jeans after allowing discount is 60 percent.

a. To find the percent of discount, we need to calculate the actual discount and divide it by the original price, then multiply by 100. From the given information, the original price of the jeans is $39.99 and the discount is $10.00. Therefore, the actual discount is $10.00 and the original price is $39.99. The percent of discount to the nearest percent is:

Percent of discount = (actual discount / original price) x 100

Percent of discount = (10.00 / 39.99) x 100

Percent of discount = 25%

Therefore, the percent of discount to the nearest percent is 25%.

b. To find the percent of sales tax, we need to divide the sales tax by the subtotal, then multiply by 100. From the given information, the subtotal is $29.99 and the sales tax is $1.95. Therefore, the percent of sales tax to the nearest tenth of a percent is:

Percent of sales tax = (sales tax / subtotal) x 100

Percent of sales tax = (1.95 / 29.99) x 100

Percent of sales tax = 6.5%

Therefore, the percent of sales tax to the nearest tenth of a percent is 6.5%.

c. The price of the jeans includes a 60% markup, which means that the selling price is 160% of the cost price. Let x be the cost price of the jeans. Then, the selling price of the jeans is 1.6x. After the discount of $10.00, the selling price becomes 1.6x - 10.00. The percent of markup after the discount to the nearest percent is:

Percent of markup = ((selling price - cost price) / cost price) x 100

Percent of markup = (((1.6x - 10.00) - x) / x) x 100

Percent of markup = (0.6x - 10.00) / x x 100

Percent of markup = 60 - (1000 / x)

Percent of markup = 60%.

So, the percent of markup after the discount is approximately 60%.

f(x)=2× if x<0
|x| if x>0

Answers

If the question is about graphing the piecewise-defined function, the attached image shows it.

The graph is in two parts: graph y = 2^x, but use only the part which is to the right of the y-axis (for x > 0), and the other part is the graph of y = |x| which lies to the left of the y-axis (for x < 0).

The open circles are to indicate that the function has no assigned value at x = 0.

Help with this math question

Answers

FG/EG = EG/DG

4/7 = 7/DG ⇒ DG = 7*7/4 = 12.25

Triangle DGE is similar to Triangle EGF, so the corresponding side lengths are proportional.

Thus, 4/7 = 7/DG. To solve for DG, invert both sides of this equation:

7/4 = DG/7

and then multiply both sides of this last equation by 7, to eliminate 7 from the denominator of DG/7:

49/4 = DG

The length of side DG is 49/4.

On Monday, a local hamburger shop sold a combined total of 556 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Monday?

Answers

h = number of hamburgers sold.
c = number of cheeseburgers sold.

we know that "c" is three times the number of "h", thus c = 3h

we also know, the total amount sold for both is 556, h + c = 556

h + c = 556
c = 3h
thus

h + (3h) = 556 <---- solve for "h" to see how many hamburgers were sold.

what about "c"? well, c = 3h

The number of cheeseburgers sold is three times the number of hamburgers sold...

c=3h

The total number sold is:

c+h=556, using c found earlier in this equation gives you:

(3h)+h=556

4h=556 divide both sides by 4

h=139

So 139 hamburgers were sold on Monday.

find the x-intercepts of the parabola with vertex (2,13) and y intercept (0,5)
round to the nearest hundredth
i have no idea how to do this problem please help!

Answers

To get the x-intercept we need the equation of the parabola;
the vertex form of the equation is given by:
y=a(x-h)^2+k

where:
(2,13) is the vertex:
Therefore;
y=a(x-2)^2+13
when x=0, y=5
Therefore the value of a will be:
5=a(0-2)^2+13
5-13=4a
4a=-8
a=-2
therefore the equation of the parabola will be:
y=-2(x-2)^2+13
y=-2x^2+8x+5
the x-intercept will be:
x=2-sqrt(7.5)
or
x=2+sqrt(7.5)

Answer:

What is the vertex of the parabola?

Round to the nearest hundredth.

✔ (8.33, 236.67)

Step-by-step explanation:

The sum of 5 consecutive even number is 100 the middle number is

Answers

100/5 =20

16 + 18 +20 +22 +24 = 100

middle number is 20

On average, Donna's Cafe has 84 customers, which represents 24% of the total approved occupancy by the fire department. a. What is the total approved occupancy of the cafe by the fire department?

Answers

well, let's say is "x", so "x" is the 100%, now if 84 is the 24%, what is "x"?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 84&24\\ x&100 \end{array}\implies \cfrac{84}{x}=\cfrac{24}{100}[/tex]

solve for "x".

Hans's vegetable garden has an area of 400 ft2. It is the shape of a rectangle with a length of 40 ft and a width of 10 ft. He has decided to expand the garden to make room for several new varieties of lettuce. The new garden will be a larger rectangle. He plans on making the new length 3 times the current length and the new width 3 times the current width.

Answers

so it will be 120ft by 30ft, is that the answer to your question?

To calculate the new area of Hans's expanded garden, multiply the new length by the new width. The new garden will have an area of 3600 ft^2.

The original garden area is 400 ft2, with a length of 40 ft and a width of 10 ft.

To find the new garden's area after expansion:

Calculate the new length: 40 ft * 3 = 120 ft.Calculate the new width: 10 ft * 3 = 30 ft.Multiply the new length by the new width: 120 ft * 30 ft = 3600 ft2.

The number of chicken legs depends on how many chickens are in the coop. This is modeled by y=2x and is an example of _____ variation.

Answers

this is an example of direct variation

Answer:

y=2x is an example of direct variation.

Step-by-step explanation:

Direct variation is mathematical relationship in between two variables which can be expressed by an equation where one variable is equal to a constant multiplied by the other variable.

In the equation y=2x, x and y are the variables and 2 is a constant.

Here it is expressed as an equation where the variable y is equal to the constant 2 multiplied by the other variable x.

Thus we can say that it is an example of direct variation.

To be eligible for a basketball tournament, a basketball team must win at least 60% of its remaining games. If the team has 21 game remaining, how many games must the team win to qualify for the tournament?

Answers

They would have to win 12.6 games. You need to find 60% of 21

Final answer:

The basketball team must win at least 13 out of their 21 remaining games to qualify for the tournament, as they need to win at least 60% of the games.

Explanation:

To determine how many games a basketball team must win out of 21 to qualify for a tournament, given they must win at least 60%, we perform the following calculation:

First, multiply the total number of remaining games, which is 21, by 60% (or 0.60) to find the minimum number of games they need to win.Next, solve for the number: 21 games × 0.60 = 12.6.Since a team can't win a fraction of a game, they must win at least the next whole number of games, which is 13.

Therefore, the team must win at least 13 games out of the remaining 21 to be eligible for the tournament.

Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.

a.Divide all terms in the equation by a.
b.Subtract the constant (the term without an x) from both sides.
c.Add a constant (in terms of a and b) that will complete the square.
d.Take the square root of both sides of the equation.
e.Solve for x.

Answers

Everyone should do this derivation, because otherwise the "quadratic formula" is some sort of "magic" LOL...

ax^2+bx+c=0

x^2+bx/a+c/a=0

x^2+bx/a=-c/a

x^2+bx/a+b^2x/(4a^2)=b^2/(4a^2)-c/a

(x+b/(2a))^2=(b^2-4ac)/(4a^2)

x+b/(2a)=±√(b^2-4ac)/(2a)

x=-b/(2a)±√(b^2-4ac)/(2a)

x=(-b±√b^2-4ac)/(2a)

Answer:

See below.

Step-by-step explanation:

We are going to take the quadratic formula ax²+bx+c=0

a.Divide all terms in the equation by a.

[tex]\frac{ax^{2} }{a} +\frac{b}{a}x+\frac{c}{a}=0\\\\x^{2} +\frac{b}{a}x+\frac{c}{a} =0[/tex]

b.Subtract the constant (the term without an x) from both sides.

[tex]x^{2} +\frac{b}{a}x+\frac{c}{a} -\frac{c}{a} =\frac{-c}{a} \\\\x^{2} +\frac{b}{a}x=-\frac{c}{a}[/tex]

c.Add a constant (in terms of a and b) that will complete the square.

[tex]x^{2} +\frac{b}{a}x=-\frac{c}{a}\\\\[tex]x^{2} +\frac{b}{a}x+\frac{b^{2} }{4a^{2} } =-\frac{c}{a} +\frac{b^{2} }{4a^{2}}\\\\(x+\frac{b}{2a}) ^{2} =\frac{-4ac+b^{2} }{4a^{2} }[/tex]

d.Take the square root of both sides of the equation.

[tex]x+\frac{b}{2a} =[tex]\\x+\frac{b}{2a} =\frac{\sqrt{-4ac+b^{2} } }{2a}\\x=\frac{\sqrt{-4ac+b^{2} } }{2a}-\frac{b}{2a} [/tex]

e.Solve for x.

[tex]x=-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]

Solve the equation for a. 55a – 44a = 11

Answers

55a-44a=11 combine like terms on the left side

11a=11 divide both sides by 11

a=1

55a - 44a = 11
11a = 11
a = 1

Sonya can walk 6 km in 3 hours. If she has to walk 10 km, how much time will it take her?

Answers

it will take sonya 20 hours

The area of Desert A is nine times the area of Desert B. If the sum of their areas is 2,000,000 square miles, find the area of each desert.

Answers

a=9b

a+b=2000000, using a from above we have:

9b+b=2000000 combine like terms on left side

10b=2000000 divide both sides by 10

b=200000, since a=9b

a=1800000

A=1,800,000 mi^2 and B=200,000 mi^2

Lowell bought 4 1/4 pounds of apples and 3 3/5 pounds of oranges. How many pounds of fruit did lo buy?

Answers

Answer:

7.85 pounds (or 7 17/20 pounds)

Step-by-step explanation:

In decimal, the total is ...

4.25 + 3.60 = 7.85 . . . pounds

As mixed numbers, the total is ...

(4 +1/4) + (3 +3/5) = (4 +3) + (1/4 +3/5) = 7 +(5/20 +12/20) = 7 17/20 . . . pounds

Lowell bought 7 17/20 pounds of fruit.

_____

Comment on the math

Any calculator can add these numbers for you. You may have to enter them as (4+1/4) and (3+3/5) if your calculator does not support mixed number entry. Depending on the calculator, you may be able to get it to show you the mixed number result. If you want a mixed number and you get a decimal number, you may have to reduce the fraction yourself:

7 85/100 = 7 17/20 . . . . . . a factor of 5/5 can be removed from the fraction

___

Any two fractions can always be added using the formula ...

a/b + c/d = (ad +bc)/(bd)

Here, that means the sum of 1/4 and 3/5 is ...

1/4 + 3/5 = (1·5 +4·3)/(4·5) = (5+12)/20 = 17/20 . . . . . the result above

In some cases, you may have to reduce the resulting fraction.

Final answer:

Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of fruit.

Explanation:

To find the total weight of fruit Lowell bought, we need to add the weights of the apples and oranges together.

Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of apples and [tex]3 \frac{3}{}[/tex] pounds of oranges. To add these fractions, we need to find a common denominator, which in this case is 20.

Converting both fractions to twentieths, we have [tex]\frac{17}{20}[/tex] pounds of apples and [tex]\frac{68}{20}[/tex] pounds of oranges. Adding these together, we get a total of [tex]\frac{85}{20}[/tex] pounds. Simplifying the fraction, we find that Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of fruit.

Learn more about Weight of fruit here:

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